# Centered tetrahedral number

We are given integer n, we need to find n-th centered tetrahedral number.**Description:** The centered tetrahedral number is a centered figurate number that represents a tetrahedron.**Tetrahedral Numbers: **A number is termed as a tetrahedral number if it can be represented as a pyramid with a triangular base and three sides, called a tetrahedron. The nth tetrahedral number is the sum of the first n triangular numbers. **The first few centered tetrahedral number** series are:

1, 5, 15, 35, 69, 121, 195, 295, 425, 589……………………….

Mathematical nth Term of centered tetrahedral number:

**Examples :**

Input : n = 3 Output : 35 Input : n = 9 Output : 589

Below is the implementation of above formula.

## C++

`// C++ Program to find nth` `// Centered tetrahedral number` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find centered` `// Centered tetrahedral number` `int` `centeredTetrahedralNumber(` `int` `n)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered tetrahedral number` ` ` `// and return it into main function.` ` ` `return` `(2 * n + 1) * (n * n + n + 3) / 3;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `n = 6;` ` ` `cout << centeredTetrahedralNumber(n);` ` ` `return` `0;` `}` |

## Java

`// Java Program to find nth Centered` `// tetrahedral number` `import` `java.io.*;` `class` `GFG {` ` ` `// Function to find centered` ` ` `// Centered tetrahedral number` ` ` `static` `int` `centeredTetrahedralNumber(` `int` `n)` ` ` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Centered tetrahedral number` ` ` `// and return it into main function.` ` ` `return` `(` `2` `* n + ` `1` `) * (n * n + n + ` `3` `) / ` `3` `;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `n = ` `6` `;` ` ` `System.out.println(` ` ` `centeredTetrahedralNumber(n));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## Python3

`# Python program to find nth` `# Centered tetrahedral number` `# Function to calculate` `# Centered tetrahedral number` `def` `centeredTetrahedralNumber(n):` ` ` `# Formula to calculate nth` ` ` `# Centered tetrahedral number` ` ` `# and return it into main function` ` ` ` ` `return` `(` `2` `*` `n ` `+` `1` `) ` `*` `(n ` `*` `n ` `+` `n ` `+` `3` `) ` `/` `/` `3` `# Driver Code` `n ` `=` `6` `print` `(centeredTetrahedralNumber(n))` ` ` `# This code is contributed by ajit ` |

## C#

`// C# Program to find nth Centered` `// tetrahedral number` `using` `System;` `class` `GFG {` ` ` `// Function to find centered` ` ` `// Centered tetrahedral number` ` ` `static` `int` `centeredTetrahedralNumber(` `int` `n)` ` ` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Centered tetrahedral number` ` ` `// and return it into main function.` ` ` `return` `(2 * n + 1) * (n * n + n + 3) / 3;` ` ` `}` ` ` ` ` `// Driver Code` ` ` `public` `static` `void` `Main ()` ` ` `{` ` ` `int` `n = 6;` ` ` `Console.WriteLine(` ` ` `centeredTetrahedralNumber(n));` ` ` `}` `}` `// This code is contributed by anuj_67.` |

## PHP

`<?php` `// PHP Program to find nth` `// Centered tetrahedral number` `// Function to find centered` `// Centered tetrahedral number` `function` `centeredTetrahedralNumber(` `$n` `)` `{` ` ` `// Formula to calculate nth` ` ` `// Centered tetrahedral number` ` ` `// and return it into main function.` ` ` `return` `(2 * ` `$n` `+ 1) *` ` ` `(` `$n` `* ` `$n` `+ ` `$n` `+ 3) / 3;` `}` `// Driver Code` `$n` `= 6;` `echo` `centeredTetrahedralNumber(` `$n` `);` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// Javascript program to find nth Centered` `// tetrahedral number` `// Function to find centered` `// Centered tetrahedral number` `function` `centeredTetrahedralNumber(n)` `{` ` ` ` ` `// Formula to calculate nth` ` ` `// Centered tetrahedral number` ` ` `// and return it into main function.` ` ` `return` `(2 * n + 1) * (n * n + n + 3) / 3;` `}` `// Driver Code` `// Given Number` `var` `n = 6;` `document.write(centeredTetrahedralNumber(n));` `// This code is contributed by Kirti` ` ` `</script>` |

**Output :**

195

**Time Complexity:** O(1)**Auxiliary Space:** O(1)

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